Why do we study euclidean geometry

These kinds of things also come up in complex analysis Schramm Loewner theory in particular , where one is trying to prove regularity results about complicated limits of stochastic processes.

It helps to think of your domain as a packing of circles, and then look at conformal maps of this. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Is Euclidean Geometry studied at all? Ask Question. Asked 6 years, 9 months ago. Active 6 years, 9 months ago. Viewed 1k times. Highly recommend it In short, will anyone see or study Euclidean geometry after high school?

Faraz Masroor Faraz Masroor 1, 1 1 gold badge 10 10 silver badges 23 23 bronze badges. The relevance of this remark to decide of the interest of mathematicians seems nearly null. More specifically, the philosophical errors involved are traceable to Piaget. Piaget was interested in analyzing the structures of the learner's mind.

Piaget claimed an affinity between such structures and the structures of "modern" mathematics. Such an identification was a non-sequitur but it influenced people like Begle who were in key positions in the US to affect pre-university education.

While talking about proofs, I notice that nobody is mentioning the conditions: while performing mathematics you can't just do what you want: all conditions need to be fulfilled before you can actually do something.

When explaining a proof to a class, it's very important that the teacher mentions the conditions, and while writing the proof, the teacher should clearly indicate at what point the mentioned conditions are used e.

This way of working learns the students why the conditions are so important and automatically they will watch their steps while setting up complicated reasonings not only in math, by the way. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Is Euclid dead? Ask Question. Asked 7 years, 6 months ago. Active 4 years ago. Viewed 6k times. Improve this question. Community Bot 1.

Yiorgos S. Smyrlis Yiorgos S. Smyrlis 4 4 silver badges 7 7 bronze badges. That is, Euclidean geometry was taken out of the syllabus about 5ish years ago, then reinstated 2 years ago. By Euclidean program, I mean the process of proving his own theorems from his postulates.

My opinion is that students should master Euclidean geometry but Euclid's program should be reserved for discussions of historical context. Nearly all of his first principles can be proved with algebra, and algebraic arguments should be heavily incorporated into curricula that explore Euclidean geometry.

Add a comment. Active Oldest Votes. Improve this answer. Toscho Toscho 3, 10 10 silver badges 15 15 bronze badges. It's clear, that the abstract proofs in Euclidean Geometry, which often use non-direct arguments, are a mere but good intermediate step in this spiral. I think I accurately connected one point of view on proof with the research justifications it rests on.

But I am willing to listen to constructive criticism. This is a centuries-old tradition dating back to the medieval quadrivium. If you look at the contents of the trivium and quadrivium, it's pretty clear that it's not meant to be utilitarian; rather, it's meant to teach you how to think and argue.

But I think the adult makeup of Lincoln, determined to learn, in flagrant opposition to all those around him as he grew up, would have been pretty robust in the face of hypothetical perturbation. Even with a grounding in Euclidean proof, I found proving basic algebraic properties from axioms to be a little strange, until I was shown some basic examples. These claims can seem so obvious that the student wonders what there even is to prove.

This specific problem must be addressed head-on before such a student is comfortable doing such exercises. I have noticed students trying to prove basic facts with examples in different countries; I think it is a natural tendency.

Van Hiele claimed it was an early developmental stage in learning to prove. I don't think it means students can't reason; they're just showing the answer is intuitively reasonable. But give students a surprising, non-obvious theorem, such as all angles inscribed in a semi-circle are right, and students tend to approach such proofs more thoughtfully. My main complaint is what Toscho sees as an good feature. In particular: Loss of Calculations Ok, fair enough, standard EG following in the steps of the long dead Euclid proceeds from Axioms to Theorem with out so much as a number in sight.

From a student's perspective, what I think is a more accurate portrait of EG is this: Artificial loss of calculations Ok, so, I can't trisect an angle. James S. Cook James S. Cook 9, 1 1 gold badge 26 26 silver badges 58 58 bronze badges. Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile.

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Develop and improve products. List of Partners vendors. Share Flipboard Email. Deb Russell. Math Expert. Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels. However, even if this course does not provide you with theorems that are directly applied in later courses, it is a good way to get used to the non-Euclidean way of thinking.

You will have to do this at some point if you want to understand modern geometry or theoretical physics. If you do so now, you will make your life easier later. Even if you have no intention of studying geometry or physics at Part II or beyond, it is worth understanding non-Euclidean geometry because its development was of fundamental importance not just to mathematics, but also to philosophy and the history of ideas.

A brief indication of why can be found here.